A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators
We prove the Schrödinger operator with infinitely many point interactions in R d ( d = 1 , 2 , 3 ) is self-adjoint if the support Γ of the interactions is decomposed into infinitely many bounded subsets { Γ j } j such that inf j ≠ k dist ( Γ j , Γ k ) > 0 . Using this fact, we prove the self-adjo...
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| Veröffentlicht in: | Annales Henri Poincaré 2020-02, Vol.21 (2), p.405-435 |
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| container_title | Annales Henri Poincaré |
| container_volume | 21 |
| creator | Kaminaga, Masahiro Mine, Takuya Nakano, Fumihiko |
| description | We prove the Schrödinger operator with infinitely many point interactions in
R
d
(
d
=
1
,
2
,
3
)
is self-adjoint if the support
Γ
of the interactions is decomposed into infinitely many bounded subsets
{
Γ
j
}
j
such that
inf
j
≠
k
dist
(
Γ
j
,
Γ
k
)
>
0
. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson–Anderson type. |
| doi_str_mv | 10.1007/s00023-019-00869-1 |
| format | Article |
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R
d
(
d
=
1
,
2
,
3
)
is self-adjoint if the support
Γ
of the interactions is decomposed into infinitely many bounded subsets
{
Γ
j
}
j
such that
inf
j
≠
k
dist
(
Γ
j
,
Γ
k
)
>
0
. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson–Anderson type.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-019-00869-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Classical and Quantum Gravitation ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Operators (mathematics) ; Original Paper ; Perturbation ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2020-02, Vol.21 (2), p.405-435</ispartof><rights>Springer Nature Switzerland AG 2019</rights><rights>2019© Springer Nature Switzerland AG 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-c58573e5a11554453c1aa29241b1335acce691c8c1bae5360c8d40816dc6aec3</citedby><cites>FETCH-LOGICAL-c319t-c58573e5a11554453c1aa29241b1335acce691c8c1bae5360c8d40816dc6aec3</cites><orcidid>0000-0002-0790-2969</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00023-019-00869-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-019-00869-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Kaminaga, Masahiro</creatorcontrib><creatorcontrib>Mine, Takuya</creatorcontrib><creatorcontrib>Nakano, Fumihiko</creatorcontrib><title>A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>We prove the Schrödinger operator with infinitely many point interactions in
R
d
(
d
=
1
,
2
,
3
)
is self-adjoint if the support
Γ
of the interactions is decomposed into infinitely many bounded subsets
{
Γ
j
}
j
such that
inf
j
≠
k
dist
(
Γ
j
,
Γ
k
)
>
0
. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson–Anderson type.</description><subject>Classical and Quantum Gravitation</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Operators (mathematics)</subject><subject>Original Paper</subject><subject>Perturbation</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEYhQdRsFZfwFXAdTT_5NKZZSleChXFdh_STMZOmSZjkiJ9BR_IF_DFzFipO1cJJ-d8gS_LLoFcAyGjm0AIySkmUGJCClFiOMoGwHKGiRBwfLjT0Wl2FsKaEMgLWg6yjzGam7bGqlq7xkZrQkAT30TjG2dR7TyKK4PmeuW_PqvGvhqPnjrjVUwv701coamtG5v67Q49KrtDzz0mpYmgdEyQgJSt0DQGNO66ttGqD1F06CXlbnPAhfPspFZtMBe_5zBb3N0uJg949nQ_nYxnWFMoI9a84CNquALgnDFONSiVlzmDJVDKldZGlKALDUtlOBVEFxUjBYhKC2U0HWZXe2zn3dvWhCjXbutt-lHmlAlWJmE8tfJ9S3sXgje17HyzUX4ngcheudwrl0m5_FEuIY3ofhRSuXf1h_5n9Q0eloaU</recordid><startdate>20200201</startdate><enddate>20200201</enddate><creator>Kaminaga, Masahiro</creator><creator>Mine, Takuya</creator><creator>Nakano, Fumihiko</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0790-2969</orcidid></search><sort><creationdate>20200201</creationdate><title>A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators</title><author>Kaminaga, Masahiro ; Mine, Takuya ; Nakano, Fumihiko</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-c58573e5a11554453c1aa29241b1335acce691c8c1bae5360c8d40816dc6aec3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Operators (mathematics)</topic><topic>Original Paper</topic><topic>Perturbation</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kaminaga, Masahiro</creatorcontrib><creatorcontrib>Mine, Takuya</creatorcontrib><creatorcontrib>Nakano, Fumihiko</creatorcontrib><collection>CrossRef</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kaminaga, Masahiro</au><au>Mine, Takuya</au><au>Nakano, Fumihiko</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2020-02-01</date><risdate>2020</risdate><volume>21</volume><issue>2</issue><spage>405</spage><epage>435</epage><pages>405-435</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>We prove the Schrödinger operator with infinitely many point interactions in
R
d
(
d
=
1
,
2
,
3
)
is self-adjoint if the support
Γ
of the interactions is decomposed into infinitely many bounded subsets
{
Γ
j
}
j
such that
inf
j
≠
k
dist
(
Γ
j
,
Γ
k
)
>
0
. Using this fact, we prove the self-adjointness of the Schrödinger operator with point interactions on a random perturbation of a lattice or on the Poisson configuration. We also determine the spectrum of the Schrödinger operators with random point interactions of Poisson–Anderson type.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-019-00869-1</doi><tpages>31</tpages><orcidid>https://orcid.org/0000-0002-0790-2969</orcidid></addata></record> |
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| ispartof | Annales Henri Poincaré, 2020-02, Vol.21 (2), p.405-435 |
| issn | 1424-0637 1424-0661 |
| language | eng |
| recordid | cdi_proquest_journals_2346496615 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Mathematical and Computational Physics Mathematical Methods in Physics Operators (mathematics) Original Paper Perturbation Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Theoretical |
| title | A Self-adjointness Criterion for the Schrödinger Operator with Infinitely Many Point Interactions and Its Application to Random Operators |
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